Fast dihedral symmetry operations on digital images in the compressed domain

We describe fast algorithms for lossless dihedral symmetry operations (rotations by ninety degrees, flips, etc.) on JPEG images. The JPEG format is widely used in digital still cameras, and these algorithms find natural applications both embedded in the camera itself and in the driver software. Current compressed domain approaches for dihedral symmetry operations typically operate on full 8×8 coefficient blocks. Our techniques for these operations use (with linear complexity) only the non-zero quantized coefficients directly in their JPEG zig-zag order, thus achieving large speed-ups as only a small number (typically less than 5) of the 64 coefficients are usually non-zero